Simplify Square Root of 40022

What is the square root of 40022 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√40022 = A√B

Unfortunately, the square root of 40022 cannot be simplified. Thus, here is the answer to the square root of 40022 in its simplest form:

√ 40022 = √ 40022

Here are two different methods we used to determine why the square root of 40022 cannot be simplified.

1) To be able to simplify the square root of 40022, one of the factors of 40022 other than 1 must be a perfect square. The factors of 40022 are 1, 2, 20011, and 40022. Since none of these factors are perfect squares, the square root of 40022 cannot be simplified.

2) To be able to simplify the square root of 40022, all the prime factors of 40022 cannot be unique. When we did prime factorization of 40022, we found that 2 x 20011 equals 40022. Since all the prime factors are unique, the square root of 40022 cannot be simplified.

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